A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states, w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the state-distinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.
@article{arxiv.quant-ph/0701126,
title = {Quantum t-designs: t-wise independence in the quantum world},
author = {Andris Ambainis and Joseph Emerson},
journal= {arXiv preprint arXiv:quant-ph/0701126},
year = {2007}
}
Comments
19 pages, v2 two references added, to appear in Complexity'06